Looking Beyond the Overall Scores of NAEP Assessments: Applications of Generalized Linear Mixed Modeling for Exploring Value-Added Item Difficulty Effects

The central idea of differential item functioning (DIF) is to examine differences between two groups at the item level while controlling for overall proficiency. This approach is useful for examining hypotheses at a finer-grain level than are permitted by a total test score. The methodology proposed in this paper is also aimed at estimating differences at the item rather than the overall score level, yet with the innovation where item-level differences for many groups simultaneously are the focus. This is a straightforward generalization of DIF as variance rather than one or several group differences; conceptually, this can be referred to as item difficulty variation (IDV). When instruction is of interest, and "groups" is a unit at which instruction is determined or delivered, then IDV signals value-added effects that can be influenced by either demographic or instructional variables.